Question-9

Let \(u=(1,1,1)\) and \(v=(2,-1,4)\) be two vectors. If \(cu+3v=(4,j,k)\), where \(c,j,k\) are real numbers, find the value of \(c\), \(j\) and \(k\).

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\[ \begin{aligned} cu+3v & =(4,j,k)\\ c(1,1,1)+3(2,-1,4) & =(4,j,k)\\ (c+6,c-3,c+12) & =(4,j,k)\\ \implies c & =-2\\ \implies j & =-5\\ \implies k & =10 \end{aligned} \]